Section A: Practice Problems Reason with Shapes

Section Summary

Details

In this section, we learned to sort shapes based on attributes such the number of sides, side lengths, and whether angles were right angles. We also sorted quadrilaterals and triangles into more specific groups.

We learned that a shape can be named based on its attributes. For example:

  • If a triangle has a right angle, then it is a right triangle.

4 right triangles.

  • If a quadrilateral has 2 pairs of sides that are the same length and 4 right angles, then it is a rectangle.

5 rectangles.

  • If a quadrilateral has sides that are all the same length, then it is a rhombus.

5 rhombuses

  • If a quadrilateral has sides that are all the same length and 4 right angles, then it is a square.

4 squares.

Problem 1 (Pre-Unit)

  1. Which shapes are hexagons?

    6 different shapes labeled A to F.

  2. Draw a quadrilateral and label it Q. Draw a pentagon and label it P.

    Grid.

Problem 2 (Pre-Unit)

  1. Finish covering the rectangle with equal-sized squares.

    Diagram. Rectangle partially partitioned to show 3 rows of 6 same-sized squares.

  2. Write an addition equation showing how many small squares there are in the rectangle.

  3. Write a multiplication equation showing how many small squares there are in the rectangle.

Problem 3 (Pre-Unit)

What is the area of the figure?

Diagram. 6 sides. Top length, unknown units. Down 4 units, right 4 units, down unknown units, left 10 units, up 9 units.

Problem 4 (Pre-Unit)

Find the length of each rectangle.

  1. Ruler measuring a rectangle in centimeters, starting at 0 centimeters.
  2. Ruler measuring a rectangle in centimeters, starting at 8 centimeters.

Problem 5 (Lesson 1)

Six different shapes labeled A to F.

  1. Which shapes have 5 angles?

  2. Which shapes have all side lengths the same size?

Problem 6 (Lesson 2)

6 triangles labeled A to F.

  1. Which triangles have one right angle?

  2. Which triangles have two sides that are the same length?

Problem 7 (Lesson 3)

One of these quadrilaterals is Diego’s mystery quadrilateral.

4 quadrilaterals labeled A to D.

List some questions you would ask to figure out Diego’s mystery quadrilateral. How would the answers help you figure out which quadrilateral it is?

Problem 8 (Lesson 4)

Select all of the quadrilaterals that are rectangles.

  2. square

Problem 9 (Lesson 5)

Dot grid.

  • Draw a quadrilateral that is not a rhombus and label it A. Explain why your shape is not a rhombus.

  • Draw a quadrilateral that is not a rectangle and label it B. Explain why your shape is not a rectangle.

Problem 10 (Exploration)

Find one of each of the following shapes in the image.

Diagram with tiling.

  1. A triangle with a right angle

  2. A triangle with 3 equal sides

  3. A rhombus

  4. A rectangle

  5. A square

Problem 11 (Exploration)

Do any of the triangles have:

A 6-equidissection of a square.

  1. a right angle?

  2. two equal sides?

  3. three equal sides?